Bootstrap Method in Theoretical Physics
arXiv:2401.00350
Abstract
In the realm of contemporary physics, the bootstrap method is typically associated with an optimization-based approach to problem-solving. This method leverages our understanding of a specific physical problem, which is used as the constraints for the optimization problem, to carve out the allowed region of our physical theory. Notably, this method often yields not only precise numerical bounds for physical quantities but also offers theoretical insights into the nature of the problem at hand. The modern numerical bootstrap method has seen its greatest success in the fields of conformal field theory (via the conformal bootstrap) and Scattering amplitude (through the S-matrix bootstrap). This dissertation presents the application of the bootstrap method to matrix models (random matrices), Yang-Mills theory, and conformal field theory. We will commence with a review of the fundamental elements of these theories. Following this, we will delve into the bootstrap studies of these models.
arXiv commentZechuan Zheng's Ph.D. thesis, defended on September 15th at École Normale Supérieure (ENS), Paris
References in corpus (83)
- Bounding scalar operator dimensions in 4D CFT
- The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
- Solving the 3D Ising Model with the Conformal Bootstrap
- Conformal Partial Waves and the Operator Product Expansion
- All genus correlation functions for the hermitian 1-matrix model
- Bootstrapping Conformal Field Theories with the Extremal Functional Method
- Radial Coordinates for Conformal Blocks
- A Mellin space approach to the conformal bootstrap
- Conformal Bootstrap in Mellin Space
- Top quark condensation
- Analytic Bounds and Emergence of Physics from the Conformal Bootstrap
- Perturbative Analysis of Gauged Matrix Models
- D-particles, Matrix Integrals and KP hierachy
- The S-matrix Bootstrap II: Two Dimensional Amplitudes
- Central Charge Bounds in 4D Conformal Field Theory
- Mastering the Master Field
- A scaling theory for the long-range to short-range crossover and an infrared duality
- Conformal Invariance in the Long-Range Ising Model
- Long-range critical exponents near the short-range crossover
- Bootstrapping phase transitions in QCD and frustrated spin systems
- Quantum Regge Trajectories and the Virasoro Analytic Bootstrap
- Bootstrapping QCD: the Lake, the Peninsula and the Kink
- Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
- Large N expansion of the 2-matrix model
- Large reduction with the Twisted Eguchi-Kawai model
- Bootstrapping Matrix Quantum Mechanics
- SU(N) gauge theories in 3+1 dimensions: glueball spectrum, string tensions and topology
- Loop Equations and bootstrap methods in the lattice
- Exact Solution of the Six-Vertex Model on a Random Lattice
- On the Polyakov-Mellin bootstrap
- PyCFTBoot: A flexible interface for the conformal bootstrap
- Bootstrapping the long-range Ising model in three dimensions
- Crossing Symmetric Dispersion Relations for Mellin Amplitudes
- Casimir recursion relations for general conformal blocks
- Bootstrap for Lattice Yang-Mills theory
- Semidefinite programming relaxations for quantum correlations
- Optimal bounds and extremal trajectories for time averages in nonlinear dynamical systems
- On critical exponents without Feynman diagrams
- JuliBootS: a hands-on guide to the conformal bootstrap
- Navigator Function for the Conformal Bootstrap
- Crossing symmetry, transcendentality and the Regge behaviour of 1d CFTs
- Cornering Large- QCD with Positivity Bounds
- Recursion relation for general 3d blocks
- Q-states Potts model on a random planar lattice
- Bootstrapping More QM Systems
- The six-vertex model on random lattices
- Bootstrap bounds on D0-brane quantum mechanics
- Bootstrapping sYM correlators using integrability
- To the theory of decaying turbulence
- Null bootstrap for non-Hermitian Hamiltonians
- A Semidefinite Programming algorithm for the Quantum Mechanical Bootstrap
- Statistical Equilibrium of Circulating Fluids
- Bootstrapping Calabi-Yau Quantum Mechanics
- Bootstrap Method in Harmonic Oscillator
- Bootstrapping PT symmetric Hamiltonians
- Crossing antisymmetric Polyakov blocks + Dispersion relation
- Bootstrapping microcanonical ensemble in classical system
- Bootstrapping the Kronig-Penney Model
- 1-form symmetry versus large N QCD
- Bootstrapping Simple QM Systems
- Bounding 3d CFT correlators
- Solving anharmonic oscillator with null states: Hamiltonian bootstrap and Dyson-Schwinger equations
- Snowmass White Paper: The Analytic Conformal Bootstrap
- Entropy Constraints for Ground Energy Optimization
- Mixed Correlator Dispersive CFT Sum Rules
- Feynman Integrals from Positivity Constraints
- Quantum Many-body Bootstrap
- Lower bounds to variational problems with guarantees
- Introduction to Monte Carlo for Matrix Models
- Bootstrapping the Ising Model on the Lattice
- Bounding scattering of charged particles in 1+1 dimensions
- Large analytical functional bootstrap I: 1D CFTs and total positivity
- Perturbative contributions to Wilson loops in twisted lattice boxes and reduced models
- Skydiving to Bootstrap Islands
- Bootstrapping the deuteron
- Different Bootstrap Matrices in Many QM Systems
- Bootstrapping the Stochastic Resonance
- Anharmonic oscillators and the null bootstrap
- Random surfaces and lattice Yang-Mills
- Non-perturbative instanton effects in the quartic and the sextic double-well potential by the numerical bootstrap approach
- Variational Equations-of-States for Interacting Quantum Hamiltonians
- Perturbation Theory and the Sum of Squares
- Unify the effect of anharmonicity in double-wells and anharmonic oscillators